Chiral nematic liquid crystal droplets as a basis for sensor systems

For a series of phospholipid coated calamitic nematic liquid crystal droplets (5CB, 6CB, 7CB, E7 and MLC7023) of diameter ∼18 μm, the addition of chiral dopant leaves the sign of surface anchoring unchanged. Herein we report that for these chiral nematic droplets an analyte induced transition from a Frank–Pryce structure (with planar anchoring) to a nested-cup structure (with perpendicular anchoring) is accompanied by changes in the intensity of reflected light. We propose this system as both a general scheme for understanding director fields in chiral nematic liquid crystal droplets with perpendicular anchoring and as an ideal candidate to be utilised as the basis for developing cheap, single use LC-based sensor devices.


Contents
1. Energy comparison for rotating a LC droplet or reorienting its director field Table ST1. Table ST2. Table ST3. Figure S1. Plot demonstrating the cross-over point at which it becomes more energetically favourable to reorient the director rather than rotate the droplet.  Figure S2. Plots of the reflection spectra of 5CB doped with 7.3 wt% S1011 as a function of temperature. Figure S3. Plots of the reflection spectra of E7 doped with 8.2 wt% S1011 as a function of temperature.

Energy comparison for rotating a LC droplet or reorienting its director field
If we assume a 10 μm diameter droplet rotates at 2πs -1 : The rotational kinetic energy of the droplet is given by; , (1) The strong r 5 dependence on droplet size is because the mass of the droplet increases with r 3 and the rotational energy increases with r 2 . Table ST1. Example values of rotational kinetic energy (U r ) for a droplet of 5CB (ρ = 1.01 kgm -3 ) with droplet diameters of 10 and 20 μm.

Reorienting the director field of a droplet
Approximating the droplet to a cylinder of dimension 2r, we can then approximate this to a circular section with a cell gap of 2r. Estimating that the director switches the bulk of the droplet in ~ 2V and that the change in capacitance is ~ 50% of Δε (which is ≈ 20); As the droplet increases in radius, so does the volume of fluid in which the elastic deformation is taking place. This will follow r 3 . However, as r increases, the same elastic energy decreases and this will follow r 2 . Therefore, for a small droplet, it is easier to rotate the whole droplet than to reorient the director field.
*These values assume K ≈ 30 pN. A K ≈ 15 pN (closer to a real value for 5CB) is used below but the order of magnitude for U n remains unchanged.

Cross-over droplet size
The point at which U n = U r allows for a cross-over radius to be found; ,  Table ST3. Example values of rotational kinetic energy (U r ) and director reorientation energy (U n ) for a droplet of 5CB.  Figure S1. Plot of the cross-over point where it becomes more energetically favourable to reorient the director rather than the rotate the droplet. (a) Kinetic energy for rotation of a droplets of various sizes (U r ), (b) director reorientation energy for droplets of varying size (U n ).

V (V) U n (J)
It is clear that for droplets in the range 10 -100 μm it will always be less energetically costly to rotate the whole droplet than to reorient the director field. Whilst these calculations have been done with an assumption that K ≈ 15 pN it is highly likely a similar trend would emerge for less elastically costly materials.  Figure S2. Temperature dependent reflection spectra of 5CB doped with 7.3 wt% S1011. (a) Reflection spectra obtained as the sample is cooled from the isotropic to 25 ℃. The peak wavelength Supplementary Information S7 is 544 nm, and the full width at half maximum is 55 nm. (b) The peak wavelength plotted against temperature showing no temperature-dependence. Figure S3. Temperature dependent reflection spectra of E7 doped with 8.2 wt% S1011. (a) Reflection spectra obtained as the sample is cooled from the isotropic to 21 °C. (b) The peak wavelength plotted against temperature showing no temperature-dependence.

Videos
Video SV1. A video of a DOPC:DOPG coated droplet of MLC7023 doped with 0.53 wt% S1011 and switched with 0.1 wt% SDS.
Video SV2. A video of a DOPC:DOPG coated droplet of MLC7023 doped with 1.9 wt% R5011 and switched with 0.1 wt% SDS.
Video SV3. A video of an array of DOPC:DOPG coated droplets of MLC7023 doped with 1.9 wt% R5011 and switched with 0.1 wt% SDS.